Assorted optical solitons of the cubic and cubic quintic nonlinear
Schrödinger equation featuring beta derivative
Abstract
Although fractional and classical order cubic quintic nonlinear
Schrödinger (NS) equation and cubic nonlinear Schrödinger equation are
used simultaneously in nonlinear optics disciplines, the
fractional-order NS equations are nowadays extensively used due to their
higher coherence. The space-time fractional cubic quintic and nonlinear
cubic Schrödinger equations integrating beta derivative are significant
in modeling to nonlinear optics, photonics, plasmas, condensed matter
physics, and other domains. The fractional wave transformation is
exploited to translate the space-time fractional equations and the
optical soliton solutions in the form of exponential, trigonometric, and
hyperbolic functions with free parameters have been established in this
article by putting to use the improved Bernoulli sub-equation function
(IBSEF) approach. The shape of the solutions includes kink, periodic,
bell-shaped soliton, breathing soliton, bright soliton, and singular
kink type soliton. The physical features of the solitons have been
revealed by depicting 3D, 2D, contour, and density graphs of some of the
solutions. The results demonstrate that the IBSEF approach is simple,
straightforward, effective and that it can be applied to a wide range of
nonlinear fractional-order models in optics and communication
engineering to achieve soliton solutions.